Displaying similar documents to “An extremal property of Turán graphs.”

Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅

Sebastian Urbański (1996)

Discussiones Mathematicae Graph Theory

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The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K₅ and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K₄-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not containing K₅.

Analogues of cliques for oriented coloring

William F. Klostermeyer, Gary MacGillivray (2004)

Discussiones Mathematicae Graph Theory

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We examine subgraphs of oriented graphs in the context of oriented coloring that are analogous to cliques in traditional vertex coloring. Bounds on the sizes of these subgraphs are given for planar, outerplanar, and series-parallel graphs. In particular, the main result of the paper is that a planar graph cannot contain an induced subgraph D with more than 36 vertices such that each pair of vertices in D are joined by a directed path of length at most two.

Equitable coloring of Kneser graphs

Robert Fidytek, Hanna Furmańczyk, Paweł Żyliński (2009)

Discussiones Mathematicae Graph Theory

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The Kneser graph K(n,k) is the graph whose vertices correspond to k-element subsets of set {1,2,...,n} and two vertices are adjacent if and only if they represent disjoint subsets. In this paper we study the problem of equitable coloring of Kneser graphs, namely, we establish the equitable chromatic number for graphs K(n,2) and K(n,3). In addition, for sufficiently large n, a tight upper bound on equitable chromatic number of graph K(n,k) is given. Finally, the cases of K(2k,k) and K(2k+1,k)...

Rainbow H -factors.

Yuster, Raphael (2006)

The Electronic Journal of Combinatorics [electronic only]

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A Tight Bound on the Set Chromatic Number

Jean-Sébastien Sereni, Zelealem B. Yilma (2013)

Discussiones Mathematicae Graph Theory

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We provide a tight bound on the set chromatic number of a graph in terms of its chromatic number. Namely, for all graphs G, we show that χs(G) > ⌈log2 χ(G)⌉ + 1, where χs(G) and χ(G) are the set chromatic number and the chromatic number of G, respectively. This answers in the affirmative a conjecture of Gera, Okamoto, Rasmussen and Zhang.

Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number

Hajo Broersma, Bert Marchal, Daniel Paulusma, A.N.M. Salman (2009)

Discussiones Mathematicae Graph Theory

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We continue the study on backbone colorings, a variation on classical vertex colorings that was introduced at WG2003. Given a graph G = (V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring for G and H is a proper vertex coloring V→ {1,2,...} of G in which the colors assigned to adjacent vertices in H differ by at least λ. The algorithmic and combinatorial properties of backbone colorings have been studied for various types of backbones in a number of papers....

Vertex Colorings without Rainbow Subgraphs

Wayne Goddard, Honghai Xu (2016)

Discussiones Mathematicae Graph Theory

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Given a coloring of the vertices of a graph G, we say a subgraph is rainbow if its vertices receive distinct colors. For a graph F, we define the F-upper chromatic number of G as the maximum number of colors that can be used to color the vertices of G such that there is no rainbow copy of F. We present some results on this parameter for certain graph classes. The focus is on the case that F is a star or triangle. For example, we show that the K3-upper chromatic number of any maximal...